The length of a rectangular flower bed is 10 more than the width. The perimeter is 120 inches. Find the dimensions of the flower bed.​

Answer:

c

Step-by-step explanation:

Answer:

C is the correct answer.

Step-by-step explanation:

given: 12, 39, 21, 18, 24, 17, 12, 25

arrange them in increasing order:

12, 12, 17, 18, 21, 24, 25, 39

solve:

outlier refers to the unit which is minimum or maximum unit in the data.

Here outlier: 39

mean with the outlier:

(sum of units)/(total number) = (168)/(8) = 21

mean without outlier:

(sum of units-39)/(total number) = (168-39)/(7) = 18.4

Answer:

The answer is "0.001 ".

Step-by-step explanation:

In this question, the shot value is missing So its solution can be defined a follows:

let

shot value= 3

The chances of missing a free takeoff \(= 1- 0.90 = 0.1\)

All three free throws are probably gone\(= 0.1^3 = 0.001\)

When given two points and asked to find the equation of the line in slope-intercept form, the correct steps, the correct order is 2 , 1 , 4 , 3.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

Given that,

given two points and asked to find the equation of the line in slope-intercept form.

Find that,

what are the correct steps? Place a number next to the step to put them in order.

Explanation:

to find the equation of the line in slope intercept form form given two points.

step 1 :

find the slope.

step 2

write equation in point slope form

step 3.

pick a point form the given points , substitue it into the point slope form

step 4.

write the equation in slope intercept form by simplifying

Final Answer.

Hence , the correct order is 2 , 1 , 4 , 3.

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Check the picture below.

\(\stackrel{\textit{\large 1st rectangle}}{\stackrel{L}{16}\times\stackrel{L-6}{10}}\qquad \qquad \stackrel{\textit{\large 2nd rectangle}}{\stackrel{L-2}{14}\times\stackrel{(L-6)+3}{13}}\)

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

not a solution

Step-by-step explanation:

p > -5

Let p = -11

-11 > -5

This is a false statement

It is not a solution

Answer:

Slope is 1/5
y intercept is (0,0)

Answer:

Step-by-step explanation:

Factors  

1, 2, 3, 4, 6, 9, 12, 18, 36

Answer:

3. -21 4. 16

Step-by-step explanation:

First we are looking for what number divided by 3 equals -7.

21 divided by 3 equals 7

So we know that we need the opposite of 21 which is -21.

Insert into equation:

-21/3=-7

So this makes the equation true.

Hence, the correct answer is -21.

Now we are looking for what number divided by -4 equals -4.

-16 divided by -4 equals 4.

So we know that we need the opposite of -16 which is 16

Insert into equation:

16/-4=-4

This makes the equation true.

Hence, the correct answer is 16

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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1. The domain for which function is one-to-one and non-decreasing [3, ∞).

2. The inverse function in the domain g(x) = √x + 3

To find a domain on which f is one-to-one and non-decreasing, we need to ensure that the function is increasing or non-decreasing (i.e., it is always moving in the positive x direction) and that each value of x maps to a unique value of f(x). A function is one-to-one if it passes the horizontal line test, meaning that every horizontal line intersects the graph at most once.

1. The function f(x) = (x-3)² has a minimum value of zero at x=3, and is   increasing on the interval (-∞, 3) and (3, ∞).

Therefore, the domain on which f is one-to-one and non-decreasing is [3, ∞).

2. To find the inverse of f restricted to this domain, we can first solve for x in terms of f(x):

f(x) = (x-3)²

√f(x) = x-3 (we take the positive square root since we're restricted to the non-negative range of f(x))

x = √f(x) + 3

Now we can define the inverse function g(x) as:

g(x) = √x + 3, where x is in the range [0, ∞).

Note that we have restricted the range of g(x) to [0, ∞) since the function f(x) is non-negative for all values of x, and therefore the inverse function must also be non-negative.

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?=118°

Answer:

<6+62=180 co interior angle

<6=180-62=118°

Answer:

solution given:

<6+<62°=180°[co- interior angle]

<6=180°-62°=118°

<6=118° is your answer

The rate at which the volume of the cube is changing is 1200 in³/seconds.

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

Where:

From the question,

Given:

If, the volume of a cube is V = L³,

Then,

Substitute these values into equation 1

Hence, the rate at which the volume is changing is 1200 in³/seconds.
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From the graph drawn above, we can see the relationship between the flower arrangements and the cost of ordering each of them.

On the x axis you have the number of orders,and on the y axis you have the cost of each order. Each flower arrangement costs $5, and the cost of fare is $10. That means the cost for each order would shown as follows;

1 order = 5 + 10 (15)

2 orders = 10 + 10 (20)

3 orders = 15 + 10 (25)

4 orders = 20 + 10 (30)

5 orders = 25 + 10 (35)

6 orders = 30 + 10 (40)

7 orders = 35 + 10 (45)

8 orders = 40 + 10 (50)

Therefore, the ordered pair for this graph is as follows;

(1, 15), (2, 20), (3, 25), (4, 30), (5, 35), (6, 40), (7, 45), (8, 50)

That is, when x = 1, y = 15, when x = 2, y = 20..., and so on.

The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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Using the Fundamental Counting Theorem, it is found that there are 576 ways for the dancers to line up.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem, considering the order:

Black - Red - Black - Red - Black - Red - Black - Red

The number of ways for each is given by:

4 - 4 - 3 - 3 - 2 - 2 - 1 - 2

Hence:

\(N = 4^2 \times 3^2 \times 2^2 = 576\)

There are 576 ways for the dancers to line up.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

X=8 1/13

Y=31 11/13

Step-by-step explanation:

Answer:

x = 15

y = 63

Step-by-step explanation:

\((9x - 7) \degree + (4x - 8) \degree = 180 \degree \\ (linear \: pair \: \angle s) \\ \\ (9x - 7 + 4x - 8) \degree = 180 \degree \\\\ (13x - 15) \degree = 180 \degree \\ \\ 13x - 15 = 180 \\ \\ 13x = 180 + 15 \\ \\ 13x = 195 \\ \\ x = \frac{195}{13} \\ \\ x = 15 \\ \\ (2y + 2) \degree = (9x - 7) \degree \\ (interior \: alternate \: \angle s) \\ \\ (2y + 2) \degree = (9 \times 15 - 7) \degree\\ \\ (2y + 2) \degree = (135- 7) \degree\\ \\ (2y + 2) \degree =128 \degree \\ \\ 2y + 2 = 128 \\ \\ 2y = 128 - 2 \\ \\ 2y = 126 \\ \\ y = \frac{126}{2} \\ \\ y = 63\)

Answer:20

Step-by-step explanation:

Answer:

I think it may be a rectangular prism

Step-by-step explanation:

it looks like one

hope it helped

The values of variables a to d are

Polynomial 1

This is given as

x² - 8x + 15 = (ax + b)(cx + d)

The factors of 15 that add up to -8 are

-3 and -5

This means that

b = -3 and d = -5

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 2

This is given as

2x³ - 8x² - 24x = 2x(ax + b)(cx + d)

Divide through by 2x

x² - 4x - 12 = (ax + b)(cx + d)

The factors of -12 that add up to -4 are

2 and -6

This means that

b = 2 and d = -6

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 3

This is given as

6x² + 14x + 4 = (ax + b)(cx + d)

Factorize

(x + 2)(6x + 2) = (ax + b)(cx + d)

By comparison, we have

a = 1, b = 2. c = 6 and d = 2

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The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.

Length and slope of PQ:

The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.

Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of PQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of PQ is approximately 3√5, and its slope is -2.

Length and slope of SR:

The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.

Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-2))² + (-5 - 1)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of SR: (y₂ - y₁) / (x₂ - x₁)

= (-5 - 1) / (1 - (-2))

= -6 / 3

= -2

Therefore, the length of SR is approximately 3√5, and its slope is -2.

Length and slope of SP:

The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.

Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(0 - (-2))² + (2 - 1)²]

= √[4 + 1]

= √5

Slope of SP: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (0 - (-2))

= 1 / 2

Therefore, the length of SP is √5, and its slope is 1/2.

Length and slope of HQ:

The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.

Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of HQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of HQ is approximately 3√5, and its slope is -2.

Based on the calculations, we can conclude that both statements are correct:

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.

Summary:

Length of PQ is approximately 3√5, and its slope is -2.

Length of SR is approximately 3√5, and its slope is -2.

Length of SP is √5, and its slope is 1/2.

Length of HQ is approximately 3√5, and its slope is -2.

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If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and the value of x is -4, the value of (f + g)(- 4) is -137.

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are typically categorized into four categories. Depending on the Element: One function to one function, many functions to one function, onto function, one function to one and onto function, into function A "vertical line test" can be used to identify whether a relation is a function when looking at a graph. If a vertical line can be drawn anywhere on the graph and cross the relation twice, the relationship is not a function.

Here,

(f+g)(x)=f(x)+g(x)

f(-4)=-3*(-4)²-4-9

f(-4)=-61

g(-4)=(-4)³-3*4

g(-4)=-76

(f+g)(-4)=f(-4)+g(-4)

=-61-76

(f+g)(-4)=-137

If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and x is -4, the value of (f + g)(- 4) is -137.

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Answer: 47 17/18

Step-by-step explanation:

48 + 1/9 (-1/2)

48 - 1/18 = 47 17/18

9514 1404 393

Answer:

  ±1, ±2, ±7, ±14

Step-by-step explanation:

The rational root theorem tells you any rational roots will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

For this function, that means rational roots will be of the form ...

  ±(divisor of 14)

Those divisors are 1, 2, 7, 14. Possible rational roots are ...

  ±1, ±2, ±7, ±14

_____

Additional comment

The graph shows this function has 3 irrational roots.

Answer:

1/25

Step-by-step explanation:

days in a week is 7

odds of being born on each 7 days is equal

x born = 7 days

pr(one separate baby) = 1 ÷ 5

pr(second separate baby) = 1 ÷ 5

pr(both being born on a school day) = 1/5 × 1/5

= 1/25